A(1) Field of the Invention
The invention generally relates to devices for reproducing digitized video pictures and more particularly to a restoration circuit used in these devices for restoring erroneous picture elements by means of some restoration method.
Such a device may be a television receiver for receiving digital television pictures which are transmitted by a television broadcasting transmitter, but it may also be an apparatus for reproducing digitally stored pictures.
A(2) Description of the Prior Art
A video picture is generally assumed to be composed of an array of M.sub.1 .times.M.sub.2 picture elements. For a video picture consisting of 625 lines M.sub.1 =625 and M.sub.2 is usually 720. For the transmission of such a video picture it is subjected to a data reduction method in order to maintain the quantity of bits to be transmitted per second (bit rate) within certain limits. A data reduction method which is very frequently used is transform coding. In this method the video picture is partitioned into sub-pictures of N.times.N picture elements each; a typical value of N is four or eight. Each sub-picture is subsequently transformed by means of a two-dimensional transform into a number of so-called coefficients accurately describing this sub-picture. For more information relating to transform coding see, for example, pages 225-232 of Reference 1.
The physical significance of this two-dimensional transform is the following. Each sub-picture is considered to be a sum of a plurality of mutual orthogonal basic pictures each also consisting of N.times.N picture elements and each with its own weighting factor. It is these weighting factors, conventionally referred to as coefficients, which are obtained by means of the two-dimensional transform.
If an error occurs in one of the coefficients in the transmission channel, this has consequences for all picture elements of the relevant sub-picture. Literature describes several so-called methods of restoring erroneous signal values in general. These known restoration methods are generally also applicable to video pictures, both in one and in two dimensions. References 2 and 3 describe some of these restoration methods. Notably, the restoration method proposed in Reference 3 yields good results for video pictures.
The restoration method proposed in Reference 3 is based on the idea that a prediction picture element s(i,j) can be determined for each picture element s(i,j) which deviates to a slight extent from the picture element and which can be considered as a linear combination of weighted versions of picture elements located in the vicinity of this picture element. This vicinity will be referred to as prediction field and it is thus understood to mean the collection of those picture elements which are considered for predicting another picture element, hereinafter referred to as reference picture element. Thus, it holds for each prediction picture element that: ##EQU1## The weighting factors a(k,l) are conventionally referred to as prediction coefficients and the collection of values k,l considered represents the prediction field.
This known restoration method is also based on the idea that the prediction coefficients should not be considered to be constant throughout the picture, but only within a limited partial region which will be referred to as reference sub-picture and which consists of P.sub.1 .times.P.sub.2 picture elements. Such a reference sub-picture is chosen to be such that it comprises all erroneous picture elements of an erroneous sub-picture, enclosed by non-erroneous (correct) picture elements. This means that for each reference sub-picture the prediction coefficients should be computed again before the erroneous picture elements can be restored. For computing the prediction coefficients each erroneous picture element within the reference sub-picture is firstly replaced in a preset process by a predetermined auxiliary picture element, for example, by zero, so that an up-dated reference sub-picture is obtained. Subsequently an iteration prediction process is performed. This process comprises a coefficient prediction step in which, as far as is possible, the associated prediction picture element is determined in accordance with expression (1) for each picture element in the up-dated reference sub-picture. Since the prediction coefficients are not known, this means that each picture element is written as a function in a(k,l) of the picture elements of the prediction field chosen. If the difference between a picture element and its prediction picture element is referred to as prediction error and is indicated by e(i,j), it holds that: EQU e(i,j)=s(i,j)-s(i,j) (2)
In this expression the prediction error is thus also a function of the prediction coefficients a(k,l). By squaring all prediction errors which can be defined for the reference sub-picture and by adding them, a prediction coefficient function Q(a) is obtained which is thus defined as follows: ##EQU2## and which is a function of all prediction coefficients. Since the erroneous picture elements were initially set at zero, a first approximation can now be obtained of the set of prediction coefficients applying to the entire reference sub-picture by minimizing the prediction coefficient function Q(a). The minimum value of this prediction coefficient function Q(a) for a given prediction coefficient is obtained by differentiating this function with respect to this prediction coefficient and by setting this derivative to zero. Since this function is quadratic in these prediction coefficients, the first approximation of each prediction coefficient thus follows.
By computing a prediction picture element in accordance with expression (1) by means of these known (first approximation) prediction coefficients in a picture element prediction step, in which the picture elements to be restored are now assumed to be the unknowns, each prediction picture element becomes a function of the unknown picture elements. By determining a prediction error in accordance with expression (2) and by defining, in analogy with expression (3), a picture element function Q(x) in accordance with ##EQU3## a first approximation of the erroneous picture elements follows in a corresponding way as described above. By replacing the original erroneous picture elements in a substitution step by these first approximations, an up-dated reference sub-picture is again produced and the coefficient prediction step and the picture element prediction step can again be performed, which leads to an even more accurate approximation of the original erroneous picture elements. This can be continued until a sufficiently accurate approximation is obtained. Usually it appears that the use of this restoration method does not lead to a noticeable improvement after the third approximation of the erroneous picture elements.